Ultrafast chirped optical waveform recorder using a time microscope

ABSTRACT

A new technique for capturing both the amplitude and phase of an optical waveform is presented. This technique can capture signals with many THz of bandwidths in a single shot (e.g., temporal resolution of about 44 fs), or be operated repetitively at a high rate. That is, each temporal window (or frame) is captured single shot, in real time, but the process may be run repeatedly or single-shot. By also including a variety of possible demultiplexing techniques, this process is scalable to recoding continuous signals.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation-in-part of application Ser. No. 12/794,727, filedJun. 5, 2010, now U.S. Pat. No. 8,064,065 which is a continuation ofapplication Ser. No. 11/823,420, filed Jun. 26, 2007, now U.S. Pat. No.7,738,111 which claims the benefit of provisional Application No.60/817,159, filed Jun. 27, 2006. Application Ser. No. 11/823,420 claimsthe benefit of provisional Application No. 60/817,172, filed Jun. 27,2006.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The United States Government has rights in this invention pursuant toContract No. DE-AC52-07NA27344 between the U.S. Department of Energy andLawrence Livermore National Security, LLC, for the operation of LawrenceLivermore National Laboratory.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a measurement method and system. Moreparticularly, the present invention relates to a measurement method andsystem for capturing both the amplitude and phase temporal profile of atransient waveform or a selected number of consecutive waveforms havingbandwidths of up to about 10 THz in a single shot or in a highrepetition rate mode.

2. Description of Related Art

Continuous real time recording of ultrafast optical waveforms presentssignificant technical challenges for conventional electronicanalog-to-digital converter (ADC) technology. In general, there are twoways to record such transient waveforms: 1) increase the electricalbandwidth and sample rate, or 2) sample the waveform repetitively. Inthe latter method for example, ultrafast waveform events are reproducedand sampled repetitively. Samples from different reproductions arecombined to reconstruct the waveform. The reproduced displayed waveformis therefore made up of many acquisitions of the signal, similar to thatof an analog sampling oscilloscope. This technique does not work forsingle-shot signals. In the former method, the most obvious way toobtain more samples on the waveform is to increase the sample rate byusing faster analog-to-digital converters. However, a typicalcommercially available state-of-the-art real-time oscilloscope has aresolution on the order of about a 18 ps step response (20 GHz analogbandwidth) and a 20 ps sampling period (50 Gsample/s), making suchoscilloscopes undesirable for measuring certain optical waveforms, suchas single-shot transient signals, when the desired resolution (step orimpulse response duration referred back to the input) requires, forexample, a temporal resolution from about 1 ps down to below 100 fs.

Other high-speed detection instruments based on electron streak tubesexist. Unfortunately, these instruments are fundamentally single shot,with a limited record length and slow read out and repetition rate. Suchinstruments also face space-charge effects which severely limit theusable dynamic range to less than 3.3 bits for 1 ps pulses.

There are also a number of ultrafast pulse measurement techniques, suchas, Frequency Resolved Optical Gating (FROG), Spectral ShearInterferometry, correlation techniques, and variations on these, whichwork well to measure the shape of less than 100 fs pulses. However, suchsystems and methods have all been demonstrated as scanned systems, whichrequires a repetitive waveform, or in single-shot systems, which canonly record with limited time-bandwidth products. In addition, in thecase of single-shot FROG, or other similar systems that map the signalinto space, frame capture rates are generally limited by slow readoutcamera technology.

It should be noted that there are also time stretching concepts relatedto but dissimilar from the true temporal imaging embodiments discussedherein. One such related technique does not have an input dispersionbefore the signal is mixed, typically electro-optically with aMach-Zehnder modulator, with the chirped time lens signal. It hasdemonstrated large time magnification and fast sampling of electricalwaves, but it is limited in the minimum impulse response duration by itsGHz bandwidth opto-electronic time lens process and an inherentdispersion penalty which blurs the signal and produces fades in thefrequency response. Likewise earlier true temporal imaging systems usingelectro-optic lenses to impart a frequency chirp are also limited inbandwidth, and thus temporal resolution. In contrast, the novel alloptical system presented herein can have many THz of bandwidth and doesnot have an inherent dispersion penalty.

Accordingly, a need exists for methods and apparatus that can measureultrafast optical waveforms with a temporal resolution from about 1 psdown to below 100 fs of impulse response width in an expedient andefficient manner. Such a system can record in a single-shot window intime with ultrafast resolution and can be performed at a high repetitionrate. Such a technology, combined with one of many demultiplexingtechniques, can be used to develop a continuous, greater than THzbandwidth, real time oscilloscope. The present invention is directed tosuch a need.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a self-referenced timelensing method that includes: providing one or more desired signals;providing one or more chirped time lens pump pulses to optically mixwith the one or more desired signals; temporally magnifying theoptically mixed one or more desired signals; and measuring a time-scaledreplica of intensity and/or frequency information of the one or moredesired signals with a temporal resolution of down to about 44 fs withwaveform fidelity, precision, and dexterity better than about 5%.

Another aspect of the present invention is directed to a self-referencedtime microscope configured to provide a time-scaled replica of theintensity and/or frequency information contained in one or more receiveddesired signals.

Still another aspect of the present invention is optionally directed toa heterodyning self-referenced time microscope recording systemconfigured to provide as well as record a time-scaled replica of theintensity and/or frequency information contained in one or more receiveddesired signals.

Accordingly, the present invention provides optical and THz arrangementsand methods for capturing both the amplitude and phase of an opticalwaveform to convert frequency chirp into a time varying intensitymodulation to enable the measurement of one or more frequencies of up toabout 10 THz that change on about a 1 ps time scale. By also including avariety of possible demultiplexing techniques, such a process is alsoscalable to recoding continuous signals.

It is to be appreciated that the methods and apparatus of the presentinvention are further adapted to simultaneously convert the carrierfrequency of a signal from one region of the electromagnetic spectrum toanother. Applications include, but are not limited to: recording ofsignals that requires below about 1 ps impulse response temporalresolution; high-energy physics and high-energy density physicsexperiments; the study of ultrafast molecular dynamics;sub-diffraction-limit imaging (e.g. synthetic aperture imaging andinverse synthetic aperture imaging); and in ultra-wideband opticalcommunications.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and constitute apart of the specification, illustrate specific embodiments of theinvention and, together with the general description of the inventiongiven above, and the detailed description of the specific embodiments,serve to explain the principles of the invention.

FIG. 1 shows an example time domain plot of a pulse intensity andfrequency chirp for the present invention.

FIG. 2 a illustrates beam spreading due to paraxial diffraction.

FIG. 2 b illustrates pulse spreading due to narrow-band dispersion.

FIG. 3 a illustrates a lens in space for comparison with the lens intime of FIG. 3 b. Both impart a quadratic phase in their real spacecoordinate.

FIG. 3 b illustrates a lens in time for comparison with the lens inspace of FIG. 3 a. Both impart a quadratic phase in their real spacecoordinate.

FIG. 4 shows an example temporal imaging diagram of an ultra-fast chirppulse recording system of the present invention.

FIG. 5 show results for a chirped 1.8 nm FWHM input pulse at 1534.0 nm(229 GHz FWHM bandwidth) as produced by configurations of the presentinvention.

FIG. 6 show results for intensity of the pulse recorded single shot (3separate measurements, 240 GHz bandwidth) in comparison to a timeaveraged measurement done with a sampling oscilloscope (40 GHz detectorlimited).

FIG. 7 shows an example diagram of a beneficial system of the presentinvention simultaneously recording a time magnified version of theintensity profile.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed to a time-domain approach in which theentire spectrum is processed and captured collectively. Thus, thepresent invention provides a time-domain measurement system and methodwhich can capture both the intensity profile and the frequency chirp ofa transient optical or THz waveform or waveforms having a highrepetition rate in a single shot format. Specifically, the methods andapparatus of the present invention are adapted to simultaneously convertthe carrier frequency of a signal from one region of the electromagneticspectrum to another. This may be from one optical band to another, orbetween THz and optical bands, or between any other bands between whichsum-frequency-generation (SFG), difference-frequency-generation (DFG),or coherent higher order mixing process is possible. As long as therequired dispersion can be produced at whatever the local carrierfrequency is, temporal imaging can be achieved while simultaneouslyconverting the signal from one spectral region to another.

Such a method and system, as disclosed herein, are fundamentallydifferent than frequency domain approaches that capture a widebandsignal only after it has been sliced into many narrow channels. Insteadof trying to record the ultrafast waveform(s) directly, embodiments ofthe present invention utilize photonic processing to transform a desiredsignal into a format compatible with conventional high-speed electronicrecording systems.

Such a method and system, as disclosed herein, are also fundamentallydifferent than other time stretching systems which do not have an inputdispersion and do not balance the input, output, and focal dispersionsaccording to an imaging condition. The temporal imaging in this systemdoes not suffer from fades in the frequency response, nor introducephase shifts between frequency components, which blur the impulseresponse. The temporal imaging system(s) and method(s) of the presentinvention are capable of fs impulse response, referred back to theinput, and when combined with heterodyning can record heterodyne beatperiods on this time scale.

To determine a frequency chirp, the desired signal is mixed with anarrow band reference signal, for example a single longitudinal mode,which is directed from a separate or the same optical source from whichthe signal was generated, thus producing a heterodyne beat signal or aself-referenced heterodyne beat signal at the instantaneous frequencydifference between the desired signal being recorded and the referencefrequency. When utilizing a reference frequency derived from the sourcelaser system, spectral components are locked in phase by the lasersmode-locking process and any frequency drift in the signal is tracked bythe same drift in the reference. As another arrangement, a nonself-referenced, heterodyne reference laser can also be used, but insuch a case the phase of the beat signal drifts at a rate inverselyproportional to the linewidth of the reference laser. It is to beappreciated that such a heterodyne beat is dramatically different fromconventional heterodyning not only in terms of the higher frequenciesbeing measured (up to about 10 THz instead of below about 20 GHz), butalso in terms in the speed at which this beat is changing (on a ps timescale instead of slower than about 1 ns). It is also to be appreciatedthat such a beat signal is beyond the speed of real-time digitizers forrecordation purposes. Therefore, to record either the beat signal or theoriginal intensity profile of the ultrafast optical waveforms, suchwaveforms are magnified in time using techniques described herein, whichenables such waveforms to maintain their shape on a transformed timescale and enables such magnified waveforms to be recorded withconventional high speed electronics with the benefit of having a systeminput resolution determined primarily by the ultrafast optical frontend.

Accordingly, using hardware and techniques of the present invention, aninput signal as illustrated in FIG. 1. can be recorded. The signal canbe chirped to spread the spectrum and evenly fill a desired time frame,such as the 100 ps time frame illustrated in FIG. 1. By blocking thereference signal (e.g., the narrow band reference), a temporal image ofan input optical intensity waveform 2 (as indicated by the left verticalaxis) can be recorded. By not blocking the reference, a temporal imageof a chirped beat which changes at the same rate as the chirp 4, i.e.,the instantaneous frequency vs time information, as indicated by theright vertical axis) can be produced and recorded. Applicable bandwidthsthat can be resolved by the present application often include up toabout 300 GHz, more often up to about 10 THz with down to about 44 fsresolution and with waveform fidelity (amplitude and phase uncertainty),precision (shot-to-shot waveform reproducibility), and dexterity(A-B-A-B reproducibility) better than about 5%. Given an input fieldE_(in)(τ) expressed in a reference frame where τ=0 is the center of thepulse;

$\begin{matrix}{{E_{in}(\tau)} = {{A_{in}(\tau)}{\exp\left( {{\mathbb{i}}\left( {{\omega_{0}\tau} + \frac{b\;\tau^{2}}{2} + \phi} \right)} \right)}}} & (1)\end{matrix}$where A_(in)(τ) is the amplitude profile, ω₀ is the center carrierfrequency, and b is the chirp parameter. The instantaneous frequency ofthe waveform is ω(r)=ω₀+bτ. If this is added to the continuous wavefield;E _(ref)(τ)=A _(ref)exp(iω _(ref)τ)  (2)the resulting intensity profile is:

$\begin{matrix}{{I_{h}(\tau)} = {{{A_{in}(\tau)}}^{2} + {A_{ref}}^{2} + {2A_{ref}{A_{in}(\tau)}{{\cos\left( {{\left( {\omega_{0} - \omega_{ref}} \right)\tau} + \frac{b\;\tau^{2}}{2} + \phi} \right)}.}}}} & (3)\end{matrix}$

When the reference amplitude is close to that of the input amplitude, astrong beat is observed. When the beat is stronger than variations inthe input amplitude profile a fit of the argument in the cosine to matchthe positions of the maxima and minima determines the chirp. It is to beappreciated that an exact match of the fringe amplitudes is not requiredto determine the chirp accurately. It is only necessary to match thebeat oscillation frequencies. Higher order chirp curvature can also beincluded. In cases where there is strong modulation in the inputamplitude A_(in)(τ), a separate recording (done simultaneously, asdescribed below) of the input waveforms intensity profile can be used todetermine the amplitude of the cosine term and produce a more accuratefit.

Many numerical techniques can be used to process the captured heterodynebeat signals and acquire the desired frequency vs time information(chirp). These include, but are not limited to, direct calculation ofbeat periods from maxima and minima, least mean squared error fitting,Fourier Transform processing, Wigner Transforming, Wavelet transforms,and Sonogram approaches.

Both the input intensity profile and beat signal described above are toofast to record with a conventional photodetector and electronicdigitizer directly. The next sections describe how desired signals canbe magnified in time by the present invention before recording.

Space-Time Analogy

The temporal magnification technique of the present invention is basedon a space-time duality between how a beam of light spreads due todiffraction as it propagates in space and how pulses of light disperse(spread) as they propagate through dispersive media. As known to thoseof ordinary skill in the art, a variety of dispersive elements, such as,for example, prism systems, optical fiber, a non-linear crystal, a freespace grating, a waveguide, an arrayed waveguide grating with feedback,a volume of dispersive material (e.g., gas, solid, or liquid), an arrayof ring resonators, a Gires-Tournois interferometer (GTI), a fiber Bragggrating, and/or a planar waveguide Bragg grating can all be used togenerate dispersive delay lines and can thus be incorporated into theconfigurations and methods disclosed herein. Since the equationsdescribing narrow-band dispersion have the same mathematical form asthose for paraxial diffraction, dispersion can perform the role ofdiffraction in the temporal equivalent to an imaging system.

FIG. 2 a and FIG. 2 b illustrates the space-time duality describedabove, wherein the graphic in FIG. 2 a shows the evolution of thetransverse spatial field profile in x as it propagates in z, and FIG. 2b shows the temporal profile of a pulse as it spreads in the local timecoordinate τ as it propagates the distance ξ. Both can be seen to imparta quadratic spectral phase to their respective frequency domains, {tildeover (ε)}(k_(x),z) and A(Ω,ξ), where k_(x) is a transverse spatialfrequency component and Ω=ω−ω₀ is an optical frequency componentrelative to the carrier. In space the strength of the diffractiondepends on the distance z and the wavevector k=2πn/λ. In the timedomain, the strength of the dispersion depends on the distance ξ and thematerials (or systems) group velocity dispersion (GVD)β″=d²β(ω)/dω²|_(ω=ω) ₀ , or the total group delay dispersion (GDD) canbe written φ″=ξβ″=dτ_(g)(ω)/dω|_(ω=ω) ₀ . It should also be noted thatcombinations of different dispersive elements may be combined to cancelhigher order dispersion (spectral phase terms), satisfying thenarrow-band approximation even for extremely wide bandwidths.

There is also a one-to-one analogy between the quadratic spatial phasemodulation produced by a space lens 5, as shown in FIG. 3 a andimparting of a quadratic temporal phase (equivalent to a linearfrequency chirp), as shown by the time lens of FIG. 3 b. Any processthat can impart such a temporal phase profile can act as the time domainequivalent of a lens in space. Electro-optic and cross-phase modulationtime lenses have been demonstrated, but they generate weak lenses withshort time apertures and are thus not well suited to recording longwaveforms with the novel ultra-fast detail of the present invention.

Accordingly, a time lens is implemented herein, as shown in FIG. 3 b,through mixing of an input signal 6 with a broadband-chirped opticalpump 8 to impart a quantity of quadratic phase curvature (equivalent toa linear frequency chirp). This mixing is generated throughsum-frequency generation, difference-frequency generation, or higherorder mixing process such as, but not limited to, four wave mixing ofthe input and pump signals in a nonlinear material 9 (e.g., GaSe, ZnGeP,GaP, LiNbO3, LiTaO3, PPLN, PPSLN, PPLT, PPSLT, KNbO3, LBO, BIBO, CLBO,KTP, GaAs, GaSe, ZnGeP, GaP, Si, Silica fibers/waveguides, dopedfibers/waveguides and/or many other nonlinear materials). In space,those skilled in the art think of the focal length f for a refractivelens, as shown in FIG. 3 a, as the propagation distance required afterthe lens, for plane wave illumination that removes the imparted phasecurvature in order to focus the beam to a small spot. This focal lengthis defined in a material (often air) and at a wavelength which has thecorresponding wavevector k.

Likewise, the temporal focal length ξ_(f), as shown in the equations ofFIG. 3 b, is considered to be the propagation length required in amaterial (or system) with GVD, β″ after the time lens, for continuouswave input that removes the imparted phase curvature and thus compressesthe light to short pulses. In systems where the GVD is constant, such asthose using only one type of optical fiber, it is convenient to workwith focal length parameter ξ_(f), but in others it is simpler to justconsider the total focal GDD φ_(f)″, as shown in FIG. 3 b.

Temporal Imaging of Optical Waveforms

Analogous to its spatial-counter-part, a system that can expand (orcompress) arbitrary temporal waveforms is thus produced by cascadingdispersive propagation, time lens modulation, and further dispersivepropagation, in the proper balance according to the temporal imagingcondition

$\begin{matrix}{{{\frac{1}{\phi_{1}^{''}} + \frac{1}{\phi_{2}^{''}}} = \frac{1}{\phi_{f}^{''}}},} & (4)\end{matrix}$where φ₁″ is the input GDD, φ₂″ is the output GDD, and φ_(f)″ is thefocal GDD, respectively. The output waveform is then a temporally scaledreplica of the input waveform,

$\begin{matrix}{{{A_{out}(\tau)} \propto {{A_{in}\left( \frac{\tau}{M} \right)}{\exp\left( \frac{- {\mathbb{i}\tau}^{2}}{2M\;\phi_{f}^{''}} \right)}}},} & (5)\end{matrix}$with a magnificationM=−φ ₂″/φ₁″.  (6)

It is to be appreciated that if the GVD characteristics of the materialis constant, such GDD ratios are reduced to ratios of propagationlengths, similar to spatial imaging. The magnification of the signal intime also reduces the bandwidth of each temporal feature (pulses), butthe quadratic temporal phase in Eqn. (5) represents the fact that thechirp imparted by the time lens, divided by the magnification, remainsin the temporal image. It is also to be appreciated that such a processis completely coherent, with both the input amplitude and phase profilesbeing scaled by the magnification.

With the definition of focal GDD, φ_(f)″=(−dω/dτ)⁻¹ as given in FIG. 3b, where dω/dτ is the time lens pump pulse chirp, the results above,strictly speaking, apply to the case of sum-frequency generation (SFG)time lens mixing. In the case of difference frequency generation (DFG)mixing, or higher order processes, the spectrum of the input signal maybe inverted or the imparted chirp may have an opposite sign to that ofthe pump. Table 1 below outlines changes in the imaging condition,carrier frequency shift, and resulting magnification for the SFG and DFGcases.

TABLE 1 Time Lens Output Imaging Image Type Carrier ConditionMagnification A_(out)(τ) ∝ SFG (or EO) ω₂ = ω₁ + ω_(p) (ω₀)${\frac{1}{\phi_{1}^{''}} + \frac{1}{\phi_{2}^{''}}} = \frac{1}{\phi_{f}^{''}}$$M = {{- \frac{\phi_{2}^{''}}{\phi_{1}^{''}}} = \frac{1}{1 - \left( {\phi_{1}^{''}\text{/}\phi_{f}^{''}} \right)}}$$A_{in}\mspace{14mu}\left( \frac{\tau}{M} \right)$ DFG, Pump- Input ω₂ =ω_(p) − ω₁${\frac{- 1}{\phi_{1}^{''}} + \frac{1}{\phi_{2}^{''}}} = \frac{1}{\phi_{f}^{''}}$$M = {{+ \frac{\phi_{2}^{''}}{\phi_{1}^{''}}} = \frac{1}{1 + \left( {\phi_{1}^{''}\text{/}\phi_{f}^{''}} \right)}}$$A_{in}^{*}\mspace{14mu}\left( \frac{\tau}{M} \right)$ DFG, Input- Pumpω₂ = ω₁ − ω_(p)${\frac{1}{\phi_{1}^{''}} + \frac{1}{\phi_{2}^{''}}} = \frac{- 1}{\phi_{f}^{''}}$$M = {{- \frac{\phi_{2}^{''}}{\phi_{1}^{''}}} = \frac{1}{1 + \left( {\phi_{1}^{''}\text{/}\phi_{f}^{''}} \right)}}$$A_{in}\mspace{14mu}\left( \frac{\tau}{M} \right)$

The above are all χ⁽²⁾ nonlinear processes. It is also possible tocreate a time lens through coherent higher order processes, such as, butnot limited to χ⁽³⁾. With a strong pump the Four Wave Mixing (FWM)process E₂ ∝ χ⁽³⁾. E_(p)E_(p)E₁* produces an output at carrierχ₂=2ω_(p)−ω₁ and imparts twice the chirp rate of a DFG, Pump-Input caseabove. Two photons of the pump are combined with one photon from theinput to produce one photon for the output instead of one photon fromeach being involved. In this case the factor of two on the impartedchirp and the complex conjugate of the signal change the imagingcondition to

${\frac{- 1}{\phi_{1}^{''}} + \frac{1}{\phi_{2}^{''}}} = {\frac{2}{\phi_{f}^{''}}.}$At this focusing condition the input field A_(in)(r) will produce acomplex conjugate and time magnified output A_(out)(τ) ∝ A_(in)*(τ/M)when the magnification is M=+φ₂″/φ₁″. This is very similar to the caseof DFG pump-input parametric temporal imaging except that the effectivetime lens strength is doubled (half the focal dispersion) and thefrequency shift of the carrier is much less. A benefit of this type oftime lens mixing is that it can be very efficient over a broad spectralband without the use of periodic poling. Fabrication tolerances inperiodic poling can lead to ripple in the mixing conversion efficiency.This source of distortion does not exist in four wave mixing temporalimaging.

In an application where it's desirable for all signals to stay at awavelength in the highly utilized telecom S-, C- and L-bands, wherelarge volumes of components are produced and industry supports componentdevelopment, this FWM time lens mixing configuration has the benefit ofkeeping the output signal in these bands if the input and pump are alsoin this band. In these bands large dispersion-to-loss ratios areavailable with specialty fibers. This alleviates the need for a chirpedfiber Bragg grating at the output and removes distortions due tofabrication tolerance induced ripple in the grating delay andreflectivity.

The same physics which produces FWM also produces self phase modulation(SPM). This could distort the time lens pump pulse and cause aberrationsin the system. This problem could be minimized my using a flat topped,or super Gaussian, intensity profile for the time lens pump. SPM induceddistortions would occur on the edges of the time lens pulse and causelittle to no effect in the center where most of the energy passesthrough the time lens process.

In an ideal system, the ultimate limit to the input resolution of asystem as disclosed herein having a large magnification is the durationof the pump pulse if it is transform limited instead of chirped; e.g.,if the pump pulse (e.g., having a configured flat top or super-Gaussiantime lens pump pulse intensity profile) has a bandwidth of a 25 fs pulseand everything else is ideal, then the temporal imaging system equatesto an input resolution limit of 25 fs. The derivation of this assumes aGaussian time lens aperture and defines two elements as being resolvedwhen they are separated in time by the duration of the systems impulseresponse. Thus, if the input waveform has the same bandwidth as the timelens pump, the field of view (temporal record length) is approximatelythe duration of the chirped pump pulse. The number of resolvable pointsis therefore given by the time lens pump pulses stretch factor, thechirped pump's duration over its transform limited duration. The presentinvention also includes filtering effects due to the transmission ofvarious optical components and group velocity mismatch in the nonlinearcrystal. These filtering effects can both reduce the aperture time andblur the image, depending on their location in the system.

Efficient conversion requires phase matching of all frequency componentsin the input 6, pump 8, and output 11 signals. In the presence of groupvelocity mismatch and group velocity dispersion, this can be difficultto do over a broad bandwidth. The crystal 9 is typically required to beshorter than in narrower band applications, also reducing theefficiency. Both the input waveform 6 and pump pulse 8 are dispersed(e.g., via, for example, Fiber Bragg Gratings, or wound optical fibers)to obtain the desired time lens phase profile and to focus the imagingsystem, thus their peak intensities are reduced. These conditions areall contrary to those desired for good conversion efficiency. For agiven energy of the time lens pump pulse this results in a fundamentaltrade off between conversion efficiency in the crystal (and thus systemloss) and the maximum per pump pulse input time aperture (frame length).The present invention provides solutions using higher energy pump lasersand optical amplification. Another example arrangement is to reduce theinput time aperture per pump pulse and run the system at a higherrepetition rate.

Yet another solution is to utilize quasi-phase matched nonlinearmaterials such as, but not limited to, periodically poled lithiumniobate (PPLN) and aperiodically poled lithium niobate (A-PPLN). Muchhigher effective nonlinear susceptibility can be achieved with thesedevices than in bulk crystals. The poling period can also be chirped toobtain higher conversion efficiency in different parts of the device fordifferent wavelength ranges, thus improving the overall efficiencyacross the entire bandwidth. Waveguides can also be written into suchPPLN devices. This maintains a tighter mode confinement over a longerinteraction length, also increasing the conversion efficiency.

Turning back to the drawings, a diagram that illustrates an exemplaryembodiment of a system having an input signal sensitivity from about 5pJ down to about 5 fJ per 100 ps input frame (temporal field of view),or about 50 mW down to about 50 μW peak optical power, as constructed inaccordance with the present invention, is shown in FIG. 4. The system,designated generally by the reference numeral 50, and capable of beingdesigned as a portable compact apparatus, generally includes a signalgeneration or acquisition unit 12, an optical source 14, a fiber coupler18, a pulse picker 22, as well as a first 26 and a second 30 opticaldispersion element (such as, for example, a chirped fiber Bragg grating(used in reflection with an optical circulator or fiber coupler), or aprism or grating pair system. However, while such optical dispersiveelements are beneficial, the present invention can also utilize anydispersive material that can induce the proper amount and kind ofdispersion required for the present application, such as, for example, aconfigured pair of wound optical fibers to induce a predetermineddispersion effect.

System 50 also includes a pair of optical amplification means 34, suchas, but not limited to, Erbium doped Fiber amplifiers, a nonlinearinteraction optical device 38, such as, but not limited to, aperiodically poled Lithium Niobate waveguide or an aperiodically poledlithium niobate (A-PPLN) as discussed above, an output dispersion means42 (e.g., wound optical fiber, prism or grating pair systems, dispersivematerial, but often a chirped fiber Bragg gratings used in reflectionwith an optical circulators or fiber coupler, etc.), a detector 46, suchas, for example, a photodiode, an amplified photoreceiver, aphotomultiplier, a charge coupled device (CCD), etc., and/or any imagingdevice constructed to the design output parameters for system 50, and ananalyzing means 52, such as a real-time oscilloscope, for analyzing thetime magnified waveforms as received by detector 46. Other componentscan replace one or both of 46 and 52, such as optical streak cameras,with significant trade-offs in the bandwidth, dynamic range, andrepetition rate of the system.

The signal generation or acquisition unit 12 is configured to eitherreceive a single-pulse transient signal or a number of such pulses or isconfigured to generate said waveform from the optical source 14. It maybe configured to induce the received modulation onto a reference signaldirected from optical source 14 (as shown by the dashed path denoted bythe letter S) or directed from a separate independent source) via forexample, an integrated-waveguide interferometric modulator (e.g., aLiNbO3 Mach-Zehnder modulator), or modulating sensor unit. It may alsobe designed to generate ultrafast arbitrary waveforms from said source14, which require real-time measurement and verification as to theirprecision, accuracy, and stability. The optical source 14 itself isoften designed to be a laser, often a mode-locked laser, arranged tooutput about 100 mW of average optical power and capable of outputting awavelength range between about 800 nm and up to about 2 micron, moreoften between about 1310 nm and up to about 1650 nm so as to alsoinclude the S, C, and L bands commonly utilized in the telecom industry.Many other wavelength bands may also be used. While a number of opticalsources can be incorporated into the present invention, a beneficialsource includes a mode-locked Pritel model UOC laser system lasing at1534 nm at 620 MHz with output pulsewidths of down to about 1 ps.Another beneficial arrangement for the optical source 14 includesintegration of an octave spanning carrier-envelope locked systemcurrently under development at Massachusetts Institute of Technology(MIT). In such an arrangement, signal and pump pulses can be chosen fromslightly shifted sections of the broadband laser.

While source 14 shows one common source for improved stability, it isalso possible for separate and varied types of sources to be used. Forexample, a narrow line-width (e.g., 1 MHz or less) Distributed Feedbacklaser (DFB) laser, or tunable single-longitudinal optical sources, suchas, but not limited to, Distributed Bragg Reflectors, Sampled GratingDBRs, Grating-assisted Co-directional Couplers with Sampled Reflectors,and Vertical Cavity Surface Emitting Lasers capable of operating withinthe designed parameters may also be utilized when operating within thescope and spirit of the present invention. Narrow band sources can beused as the heterodyne reference or be modulated by an ultrafast eventas part of signal generation or acquisition unit 12. The time lens pumppulse is required to have a broad bandwidth in order to obtain goodtemporal resolution. A broadband modelocked laser source can be useddirectly or narrow band sources as mentioned earlier can be modulatedwith high speed amplitude and phase modulators to spectrally broaden thesignals. In addition, example arrangements with such sources asdisclosed herein also include utilizing soliton compression indispersion-decreasing fiber to simultaneously broaden the bandwidth andshift the wavelength (e.g., to shift from 1534 nm to 1558 nm) of achosen pump signal to preclude deleterious effects, such as degeneratecollinear sum-frequency mixing in the non-linear crystal embodiments ofthe present invention. Other nonlinear processes such as self phasemodulation may also be used to broaden the spectrum of the pump signal.

Turning back to FIG. 4, in the method of the invention, a desiredwaveform to be recorded (not shown) is generated by the signalgeneration or acquisition unit 12. It may be by way of an inducedmodulation of an electromagnetic radiation beam directed from opticalsource 14 (as denoted by the dashed path line S), or by an ultrafastmodulation of an independent source. The induced modulated signal asproduced from signal generation or acquisition unit 12 is directed alongpath A (shown with a directional arrow). Optionally, a narrowbandreference signal (preferably generated from optical source 14 inconjunction with a filtering means 16 (e.g., one or more narrow bandfilters, edge filters, long pass and short filters, etc.)) is directedalong path B (shown with a directional arrow) for use in heterodyning(via optical coupler 18) with the induced signal directed along path A.Upon optional heterodyning, the resultant signal is further directed tothe Signal & Heterodyne reference path 19 (as shown by the dashed box),which includes being directed through optical dispersive element 26 toinduce a predetermined amount of dispersion into the signals receivedfrom optical coupler 18. Thereafter, the heterodyned signal is amplifiedvia amplifier 34 to make up for losses resulting from upstream elements.In the embodiment without heterodyning, the signal from SignalAcquisition or Generating Unit 12 is dispersed and input into nonlinearcrystal 38 along with the signal from the time-lens pump pulse path 23discussed below.

A third signal directed along path C (also denoted with an accompanyingdirectional arrow) includes a broadband pulse also generated fromoptical source 14 and is directed to the time-lens pump pulse path 23(also shown with a dashed box). As shown within the time-lens pump path23, a pulse picker 22, such as a Mach Zehnder modulator or anyelectro-optic modulator or acousto-optic modulator having a suitableelectronic driver, is configured in the pump pulse path of the exampleembodiment for system 50 to reduce the rate of the time lens pumpthereby causing, for example, only 1 out of 4 (rate adjustable) ofdesired input signals to be up-converted and recorded at the output. Thethree dispersive delay lines in the system are adjusted according totemporal imaging conditions as per equation 4, as discussed above, tofocus the system and produce a time-scaled replica at the output of thewaveform at the input with, for example a suitable temporalmagnification of up to about +/−100×. The nonlinear interaction opticaldevice 38 is configured to impart the chirp of the time lens pumpthereby generating a time lens. The FBG/Circulator (or directionalcoupler) configuration imparts the image dispersion and the timemagnified signal is received by detector 46 and captured by an availablescope capable of resolving such magnified images of the presentinvention.

The present invention will be more fully understood by reference to thefollowing examples, which are intended to be illustrative of the presentinvention, but not limiting thereof.

FIG. 5 shows results for a recorded chirped 1.8 nm FWHM input pulse 70(shown as a dashed line) at 1534.0 nm (229 GHz FWHM bandwidth) asproduced by configurations of the present invention. A CW signal at1534.7 nm is added at the input to convert the frequency chirp into thechirped heterodyne beat 70. Also shown in FIG. 5 are the calculatedoscillation frequencies 74 (shown as a series of black circles) for theadjacent minima in 70 and a linear fit 78 (shown as solid line) to matchthe positions of the maxima and minima so that the chirp can bedetermined. The pulse 70 recorded at the output had been temporallymagnified by a factor of −30.09× and recorded on a high speedphoto-receiver and an 8 GHz real time scope. The −3.45 GHz/ns chirpedbeat signal 70 recorded on the oscilloscope indicates an initial inputwith an optical frequency chirp of 312.9 GHz/100 ps. This is a 240 GHzbandwidth single shot measurement system that currently repeats at 990KHz.

FIG. 6 show results for intensity of the pulse recorded single shot (3separate measurements, 240 GHz bandwidth) in comparison to a timeaveraged measurement done with a sampling oscilloscope (40 GHz detectorlimited). In particular, this is a measurement of just the intensityprofile (only the reference is off) when the heterodyne reference isturned off using the configuration, as shown in FIG. 4. Each trace(i.e., #1, #2, and #3, as denoted by reference numerals 80, 84, and 88respectively) are obtained single-shot measurements (as referenced bythe left vertical scale) as made approximately 30 seconds apart using anexample temporal imaging magnification of −30.09×, a 12 GHz receiver,and a Tektronix TDS6804B 8 GHz scope having an effective Bandwidth of240 GHz. The resultant data 80, 84, and 88 show fast temporal detailsand changes in the signal from pulse to pulse which cannot be recordedwith a sampling scope, as referenced by the right vertical scale. Theheavy line trace 92 is a signal recorded on a repetitive, time averagedbasis with a 40 GHz photodiode and 50 GHz sampling oscilloscope. Theoverall profile matches well. The sampling scope measurement was madelater in the day and the circled region 96 level change is consistentwith changes in the laser system (e.g., drift) that were observed.Again, the temporal imaging system measurements 80, 84, and 88, asreferenced by the left vertical scale, show faster details and are eachsingle shot measurements of one pulse, whereas the data 92 referenced bythe right vertical scale is a repetitively averaged measurement of manypulses which blurs some of the faster details.

FIG. 7 shows another beneficial example system having input signalsensitivities from about 5 pJ down to about 5 fJ per 100 ps input frame(temporal field of view), or about 50 mW to 50 μW peak optical power.Such a system, designated generally by the reference numeral 700, isadapted to simultaneously record both the time magnified heterodyne beatsignal, as discussed above and as shown in FIG. 4, and a time magnifiedversion of the intensity profile. It is to be noted that commonreference numbers denoted in FIG. 4 are utilized where similarlyappropriate in FIG. 7.

For example, system 700 generally includes a signal generation oracquisition unit 12, an optical source 14, a pulse picker 22, as well asa first 26 and a second 30 optical dispersion element (such as, forexample, a chirped fiber Bragg grating (used in reflection with anoptical circulator or fiber coupler), or a prism or grating pair system.However, while such optical dispersive elements are beneficial, thepresent invention can also utilize any dispersive material that caninduce the proper amount and kind of dispersion required for the presentapplication, such as, for example, a configured pair of wound opticalfibers to induce a predetermined dispersion effect.

System 700 also includes a pair of optical amplification means 34, suchas, but not limited to, Erbium doped Fiber amplifiers, a nonlinearinteraction optical device 38, such as, but not limited to, aperiodically poled Lithium Niobate waveguide or an aperiodically poledlithium niobate (A-PPLN), an output dispersion means 42 (e.g., woundoptical fiber, prism or grating pair systems, dispersive material, butoften a chirped fiber Bragg gratings used in reflection with an opticalcirculator or fiber coupler, etc.), a detector 46, such as, for example,a photodiode, an amplified photoreceiver, a photomultiplier, a chargecoupled device (CCD), etc., and/or any imaging device constructed to thedesign output parameters for system 700, and an analyzing means 52, suchas a real-time oscilloscope, for analyzing the time magnified waveformsas received by detector 46. Other components can replace one or both of46 and 52, such as optical streak cameras, with significant trade-offsin the bandwidth, dynamic range, and repetition rate of the system.

Similar to the example configuration of FIG. 4, the signal generation oracquisition unit 12, as shown in FIG. 7, is configured to either receivea single-pulse transient signal or a number of such pulses or isconfigured to generate said waveform from the optical source 14. It maybe configured to induce the received modulation onto a reference signaldirected from optical source 14 (or directed from a separate independentsource) via for example, an integrated-waveguide interferometricmodulator (e.g., a LiNbO3 Mach-Zehnder modulator), or modulating sensorunit. It may also be designed to generate ultrafast arbitrary waveformsfrom said source 14, which require real-time measurement andverification as to their precision, accuracy, and stability. The opticalsource 14 itself is often designed to be a laser, often a mode-lockedlaser, arranged to output about 100 mW of average optical power andcapable of outputting a wavelength range between about 1310 nm and up toabout 1650 nm so as to also include the S, C, and L bands commonlyutilized in the telecom industry. Many other wavelength bands may alsobe used. While a number of optical sources can be incorporated into theconfiguration of FIG. 7, a beneficial source includes a harmonicallymode locked sigma laser lasing at 1534 nm at 620 MHz with outputpulsewidths of down to about 1 ps. Another beneficial arrangement forthe optical source 14 includes integration of an octave spanningcarrier-envelope locked system currently under development atMassachusetts Institute of Technology (MIT). In such an arrangement,signal and pump pulses can be chosen from slightly shifted sections ofthe broadband laser.

As also similarly discussed above with reference to FIG. 4, source 14 inFIG. 7 shows one common source for improved stability but it is alsopossible for separate and varied types of sources to be used. Forexample, a narrow line-width (e.g., 1 MHz) Distributed Feedback laser(DFB) laser, or tunable single-longitudinal optical sources, such as,but not limited to, Distributed Bragg Reflectors, Sampled Grating DBRs,Grating-assisted Co-directional Couplers with Sampled Reflectors, andVertical Cavity Surface Emitting Lasers capable of operating within thedesigned parameters of the present invention.

Turning exclusively to the beneficial configuration of FIG. 7, in themethod of the invention, a desired waveform to be recorded (not shown)is generated by the signal generation or acquisition unit 12. It may beby way of the induced modulation of an electromagnetic radiation beamdirected from optical source 14 or by an ultrafast modulation of anindependent source. The induced modulated signal as produced from signalgeneration or acquisition unit 12 is directed along path A (i.e., shownwith a directional arrow) and is further directed along the top legdenoted within a dashed box as Signal Path 19″). Signal path 19″ can bereferred to as the input dispersion path, which includes being directedthrough optical dispersive element 26 to induce a predetermined amountof dispersion into the directed signals received and thereafter, thesignal having an induced input dispersion is amplified via amplifier 34to make up for losses resulting from upstream elements.

The signal received form amplifier 34 is split into two paths (denotedas K and K′) by a splitter 21, often a 50/50% splitter. One such splitsignal (K′) is directed into a first time lens crystal 38′, e.g., aperiodically poled Lithium Niobate waveguide or an aperiodically poledlithium niobate (A-PPLN) waveguide. The second portion of the splitsignal (K) is received and further directed by a first coupler 18′ intoa second time lens crystal 38, e.g., a periodically poled LithiumNiobate waveguide or an aperiodically poled lithium niobate (A-PPLN)waveguide.

A middle path (i.e., Heterodyne Reference Path 19′, as shown within adashed portion) is configured to combine the signal received from anarrowband reference signal (often generated from optical source 14 inconjunction with a filtering means 16 (e.g., one or more narrow bandfilters, edge filters, long pass and short filters, etc.)) with a splitportion (K) from one of the dispersed inputs as directed from the SignalPath 19″ (i.e., after the input dispersion instead of before the inputdispersion, as in FIG. 4) via an optical coupler 18′, which can then bereceived by crystal 38 for producing a time lens output using theheterodyne reference path 19′ signal.

The very bottom leg is the path of the chirped time lens pump pulse 23,as discussed above and as shown in FIG. 4, except that it is split alongtwo paths (denoted as L and L′ by splitter 21′, often a 50/50 splitter)to drive the two mixing time lens crystals 38′ and 38 respectively. Thetop crystal path (i.e., through crystal 38′) produces the normal timelens output when there is no heterodyne reference and the bottom crystal(i.e., crystal 38) produces a time lens output for the case with theheterodyne reference. The signals are time delayed relative to eachother, (e.g., via optical delay 39) so that they do not overlap and thengo through a final coupler 41 and then a common output dispersion 42.Such an arrangement allows for the same input dispersion, outputdispersion, and time lens pump to be used on both the temporal image ofthe signal and of the heterodyned signal. Thus, the magnifications arethe same and any distortions are common to both.

U.S. application Ser. No. 12/794,727, titled: “Ultrafast Chirped OpticalWaveform Recorder Using Self-Referenced Heterodyning and a TimeMicroscope” filed Jun. 5, 2010, is incorporated herein by reference.U.S. application Ser. No. 11/823,420, filed Jun. 26, 2007, isincorporated herein by reference. U.S. Provisional Application No.60/817,159, filed Jun. 27, 2006, and U.S. Provisional No. 60/817,172,filed Jun. 27, 2006, are both incorporated herein by reference.

Applicants are providing this description, which includes drawings andexamples of specific embodiments, to give a broad representation of theinvention. Various changes and modifications within the spirit and scopeof the invention will become apparent to those skilled in the art fromthis description and by practice of the invention. The scope of theinvention is not intended to be limited to the particular formsdisclosed and the invention covers all modifications, equivalents, andalternatives falling within the spirit and scope of the invention asdefined by the claims.

The invention claimed is:
 1. A time lensing method, comprising:dispersing a non-heterodyned waveform to produce a first dispersedsignal; dispersing a signal from an optical source to produce a seconddispersed signal; mixing said first dispersed signal with said seconddispersed signal in a nonlinear material to produce a combined signal,wherein said combined signal comprises a quadratic time lens phase;dispersing said combined signal to produce a dispersed combined signal;and detecting said dispersed combined signal.
 2. The method of claim 1,further comprising providing said waveform.
 3. The method of claim 1,wherein the step of mixing said dispersed signal with said seconddispersed signal to produce a combined signal is carried out with anon-linear crystal.
 4. The method of claim 3, wherein said non-linearcrystal comprises a quasi-phase matched waveguide device.
 5. The methodof claim 4, wherein said quasi-phase matched waveguide device isselected from the group consisting of a poled Lithium Niobate crystaland an aperiodically poled lithium niobate (A-PPLN) crystal.
 6. Themethod of claim 1, wherein the step of dispersing a non-heterodynedwaveform comprises dispersing, with a first device, a non-heterodynedwaveform to produce a first dispersed signal, wherein said first deviceis selected from the group consisting of a first optical fiber, a firstnon-linear crystal, a first free space grating, a first waveguide, afirst arrayed waveguide grating with feedback, a first volume ofdispersive material, a first array of ring resonators, a firstGires-Tournois interferometer (GTI), a first fiber Bragg grating, and afirst planar waveguide Bragg grating, wherein the step of dispersing asignal comprises dispersing, with a second device, a signal from anoptical source to produce a second dispersed signal, wherein said seconddevice is selected from the group consisting of a second optical fiber,a second non-linear crystal, a second free space grating, a secondwaveguide, a second arrayed waveguide grating with feedback, a secondvolume of dispersive material, a second array of ring resonators, asecond Gires-Tournois interferometer (GTI), a second fiber Bragggrating, and a second planar waveguide Bragg grating.
 7. The timelensing method of claim 1, wherein the step of mixing comprises fourwave mixing of said first dispersed signal with said second dispersedsignal, wherein said nonlinear material comprises a material with a χ⁽³⁾nonlinearity such that E₂∝χ⁽³⁾·E_(p)E_(p)E₁*, where E₂ is the output,E_(p) is the time lens pump, and E₁* is the complex conjugate of theinput fields respectively.
 8. The time lensing method of claim 1,wherein said first dispersed signal comprises a frequency chirp largerthan the chirp rate of said second dispersed signal.
 9. The time lensingmethod of claim 1, wherein said waveform comprises a signal carrierfrequency, wherein said signal carrier frequency comprises at least oneelectromagnetic band selected from optical and THz frequencies.
 10. Themethod of claim 1, wherein said first dispersed signal comprises adispersed THz input signal.
 11. The method of claim 3, wherein saidnon-linear crystal comprises a material selected from the groupconsisting of GaSe, ZnGeP, GaP, LiNbO3, LiTaO3, PPLN, PPSLN, PPLT,PPSLT, KNbO3, LBO, BIBO, CLBO, KTP, GaAs, GaSe, ZnGeP and GaP.
 12. Atime microscope, comprising: a signal acquisition or generating unit forproviding a waveform to be recorded; an optical source for providing isfirst signal; means for dispersing said waveform to produce a firstdispersed signal, wherein there is no means for heterodyning saidwaveform between said signal acquisition or generating unit and saidmeans for dispersing said waveform; means for dispersing said firstsignal from said optical source to produce a second dispersed signal;means for mixing said first dispersed signal with said second dispersedsignal in a nonlinear material to produce a combined signal, whereinsaid combined signal comprises a quadratic time lens phase produced withcoherent higher order processes; means for dispersing said combinedsignal to produce a dispersed combined signal; and a detector fordetecting said dispersed combined signal.
 13. The time microscope ofclaim 12, wherein said means for mixing comprises one or more non-linearcrystals.
 14. The time microscope of claim 13, wherein said one or morenon-linear crystals comprise a quasi-phase matched nonlinear material.15. The time microscope of claim 14, wherein said quasi-phase matchednonlinear material comprises at least one device selected from a poledLithium Niobate waveguide and an aperiodically poled lithium niobate(A-PPLN) waveguide.
 16. The time microscope of claim 14, wherein saidone or more non-linear crystals comprise at least one non-linearmaterial selected from GaSe, ZnGeP, GaP, LiNbO3, LiTaO3, PPLN, PPSLN,PPLT, PPSLT, KNbO3, LBO, BIBO, CLBO, KTP, GaAs, GaSe, ZnGeP, and GaP.17. The time microscope of claim 12, wherein at least one of said firstmeans for dispersing and said second means for dispersing comprise atleast one dispersive element selected from an optical fiber, anon-linear crystal, a free space grating, a waveguide, an arrayedwaveguide grating with feedback, a predetermined volume of dispersivematerial, an array of ring resonators, a Gires-Tournois interferometer(GTI), a fiber Bragg grating and a planar waveguide Bragg grating. 18.The time microscope of claim 12, further comprising means for solitoncompression of said second dispersed signal.
 19. The time microscope ofclaim 12, wherein said optical source comprises a laser.
 20. The timemicroscope of claim 19, wherein said laser comprises at least one sourceselected from a mode-locked laser, an octave spanning carrier-envelopelocked laser, a Distributed Feedback laser (DFB) laser, a DistributedBragg Reflector, a Sampled Grating DBRs, and a Vertical Cavity SurfaceEmitting Laser.
 21. The time microscope of claim 19, wherein said lasercomprises a wavelength range between about 800 nm and up to about 2micron.
 22. The time microscope of claim 19, wherein said lasercomprises a wavelength range between about 1310 nm and up to about 1650nm so as to also include the S, C, and L telecommunication bands. 23.The time microscope of claim 12, wherein said second means fordispersing comprises a pulse picker.
 24. The time microscope of claim23, wherein said pulse picker comprises at least one modulator selectedfrom an electro-optic modulator and an acousto-optic modulator.
 25. Thelime microscope of claim 23, wherein said pulse picker comprises a MachZehnder modulator.
 26. A time lensing method, comprising: dispersing awaveform consisting essentially of a non-heterodyned waveform to producea first dispersed signal; dispersing a signal from an optical source toproduce a second dispersed signal; mixing said first dispersed signalwith said second dispersed signal in a nonlinear material to produce acombined signal, wherein said combined signal comprises a quadratic timelens phase; dispersing said combined signal to produce a dispersedcombined signal; and detecting said dispersed combined signal.